Weighted-L-2 Polynomial Approximation In C

arXiv: Complex Variables(2020)

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摘要
We study the density of polynomials in H-2(Omega, e(-phi)), the space of square integrable holomorphic functions in a bounded domain Omega in C, where phi is a subharmonic function. In particular, we prove that the density holds in Caratheodory domains for any subharmonic function phi in a neighborhood of (Omega) over bar. In non-Caratheodory domains, we prove that the density depends on the weight function, giving examples.
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关键词
Caratheodory domain, weighted L-2-estimates, polynomial approximation, moon-shaped domain
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